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E




Mathematica Notation

Traditional Notation









Constants > E > Product representations





http://functions.wolfram.com/02.05.08.0003.01









  


  








Input Form





E == 2 (2/1)^(1/2) ((2/3) (4/3))^(1/4) ((4/5) (6/5) (6/7) (8/7))^(1/8) ((8/9) (10/9) (10/11) (12/11) (12/13) (14/13) (14/15) (16/15))^(1/16) \[Ellipsis]








Standard Form





Cell[BoxData[RowBox[List["\[ExponentialE]", "\[Equal]", " ", RowBox[List["2", SuperscriptBox[RowBox[List["(", FractionBox["2", "1"], ")"]], FractionBox["1", "2"]], SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["2", "3"], FractionBox["4", "3"]]], ")"]], FractionBox["1", "4"]], SuperscriptBox[RowBox[List["(", " ", RowBox[List[FractionBox["4", "5"], FractionBox["6", "5"], FractionBox["6", "7"], FractionBox["8", "7"]]], ")"]], FractionBox["1", "8"]], SuperscriptBox[RowBox[List["(", " ", RowBox[List[FractionBox["8", "9"], FractionBox["10", "9"], FractionBox["10", "11"], FractionBox["12", "11"], FractionBox["12", "13"], FractionBox["14", "13"], FractionBox["14", "15"], FractionBox["16", "15"]]], ")"]], FractionBox["1", "16"]], "\[Ellipsis]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mi> &#8519; </mi> <mo> &#10869; </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mfrac> <mn> 2 </mn> <mn> 1 </mn> </mfrac> </msqrt> <mo> &#8290; </mo> <mroot> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mn> 4 </mn> </mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mn> 3 </mn> </mrow> </mfrac> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mroot> <mfrac> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mn> 6 </mn> <mo> &#8290; </mo> <mn> 6 </mn> <mo> &#8290; </mo> <mn> 8 </mn> </mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mn> 5 </mn> <mo> &#8290; </mo> <mn> 7 </mn> <mo> &#8290; </mo> <mn> 7 </mn> </mrow> </mfrac> <mn> 8 </mn> </mroot> <mo> &#8290; </mo> <mroot> <mfrac> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mn> 10 </mn> <mo> &#8290; </mo> <mn> 10 </mn> <mo> &#8290; </mo> <mn> 12 </mn> <mo> &#8290; </mo> <mn> 12 </mn> <mo> &#8290; </mo> <mn> 14 </mn> <mo> &#8290; </mo> <mn> 14 </mn> <mo> &#8290; </mo> <mn> 16 </mn> </mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mn> 9 </mn> <mo> &#8290; </mo> <mn> 11 </mn> <mo> &#8290; </mo> <mn> 11 </mn> <mo> &#8290; </mo> <mn> 13 </mn> <mo> &#8290; </mo> <mn> 13 </mn> <mo> &#8290; </mo> <mn> 15 </mn> <mo> &#8290; </mo> <mn> 15 </mn> </mrow> </mfrac> <mn> 16 </mn> </mroot> <mo> &#8290; </mo> <mo> &#8230; </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='rational'> 2 <sep /> 1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3 </cn> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <cn type='integer'> 6 </cn> <cn type='integer'> 6 </cn> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 5 </cn> <cn type='integer'> 5 </cn> <cn type='integer'> 7 </cn> <cn type='integer'> 7 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <cn type='integer'> 10 </cn> <cn type='integer'> 10 </cn> <cn type='integer'> 12 </cn> <cn type='integer'> 12 </cn> <cn type='integer'> 14 </cn> <cn type='integer'> 14 </cn> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 9 </cn> <cn type='integer'> 9 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 13 </cn> <cn type='integer'> 13 </cn> <cn type='integer'> 15 </cn> <cn type='integer'> 15 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 16 </cn> </apply> <ci> &#8230; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[ExponentialE]", "]"]], "\[RuleDelayed]", RowBox[List["2", " ", SqrtBox[RowBox[List["2", " ", FractionBox["1", "1"]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["2", " ", "4"]], RowBox[List["3", " ", "3"]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["4", " ", "6", " ", "6", " ", "8"]], RowBox[List["5", " ", "5", " ", "7", " ", "7"]]], ")"]], RowBox[List["1", "/", "8"]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["8", " ", "10", " ", "10", " ", "12", " ", "12", " ", "14", " ", "14", " ", "16"]], RowBox[List["9", " ", "9", " ", "11", " ", "11", " ", "13", " ", "13", " ", "15", " ", "15"]]], ")"]], RowBox[List["1", "/", "16"]]], " ", "\[Ellipsis]"]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29